| Summary: | <p>This thesis primarily dives into investigating the details of four-dimensional vacua within String Theory using the AdS/CFT correspondence. In the first and second part of the thesis, we study the fibred Calabi-Yau and M-theory moduli stabilization scenario. We consider both flux-stabilized models and non-perturbative stabilization methods. We perform a holographic analysis to determine the spectrum of the assumed dual <i>CFT</i><sub>3</sub> to understand its AdS/CFT implications. For the flux stabilization, which relies on a large complex Chern-Simons invariant, moduli have integer dimensions similar to the DGKT flux-stabilized model in type IIA. For the non-perturbative stabilization, the results are similar to race-track models in type IIB.<p>
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<p>In the last part of the thesis, we solve the Wheeler DeWitt equation for the planar Reissner-Nordstrom-AdS black hole in a minisuperspace approximation. We construct semiclassical Wheeler-DeWitt states from Gaussian wavepackets that are peaked on classical black hole interior solutions. By using the metric component <i>g<sub>xx</sub></i> as a clock, these states are evolved through both the exterior and interior horizons. Close to the singularity, we show that quantum fluctuations in the wavepacket become important, and therefore the classicality of the minisuperspace approximation breaks down. To- wards the AdS boundary, the Wheeler-DeWitt states are used to recover the Lorentzian partition function of the dual theory living on this boundary. This partition function is specified by an energy and a charge. Finally, we show that the Wheeler-DeWitt states know about the black hole thermodynamics, recovering the grand canonical thermody- namic potential after an appropriate averaging at the black hole horizon.</p>
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